HOLLOWAY, Chief Judge.

Defendant Francisco Larranaga timely appeals his conviction for perjury under 18 U.S.C. § 1623, pressing several grounds for reversal. We find that no reversible error was committed, and affirm.

I The factual background

This case arose out of a federal grand jury investigation of Sangre de Cristo Mental Health Center, Inc. (Sangre), Northern Community Preservation, Inc. (NCP), and David Knight. Sangre, a non-profit organization, received federal funds from the Department of Health and Human Services. IV R. 117. Its executive director, David Knight, was heavily involved in the affairs of NCP, see IV R. 118, 120, attending many of its board meetings and assisting in its accounting. V R. 367. From this connection, a close financial relationship developed between NCP and Sangre. Sangre leased three buildings and two telephone systems from NCP, the latter deriving all of its income from these rental payments. V R. 221, 264, 372.

The personnel of the two corporations overlapped. In addition to Knight's dual role, for example, Caren Stanley-Smith, a board-member of NCP, served as an employee of Sangre. Similarly, Ms. Celina Rael de Garcia, who was Director of Operations for NCP during the investigation, was also a director for Sangre and she functioned as a secretary for NCP. V R. 263-65.

The grand jury's investigation centered on a possible misuse of federal funds by Sangre. It was concerned, at least in part, with Sangre's leases from NCP. IV R. 116. Investigators believed that some of the rental payments were excessive. Gradually, the grand jury became increasingly concerned with Knight's simultaneous participation in the affairs of the two corporations. IV R. 123, 130-31, 166.

On or about February 6, 1983, Larranaga received a subpoena instructing him to bring the company's records to the grand jury on March 8, 1983. Among the requested documents was a set of the minutes for NCP's board meetings from August 31, 1981, to February 23, 1983. The only minutes then in existence, however, were a number of rough notes that had been taken at the meetings. These notes were handwritten on placemats, napkins and legal pads. Larranaga and Stanley-Smith instructed Ms. Garcia to type a set of minutes from the notes. Garcia did so; however, she apparently discarded many of the notes, returning to Larranaga only the pages she had typed. Government Exhibit 7, at 255.

Larranaga appeared before the grand jury on March 8, 1983, bringing copies of the pages Garcia had typed. Larranaga produced this set of minutes which included a minute for an October 28, 1981 NCP board meeting, listing certain persons as present but not stating that Knight was present and that he made a commitment that Sangre would continue to occupy a Las Vegas building if NCP bought it. IV R. 115; Government Exhibit 2. At a June 1, 1983 grand jury appearance Larranaga produced a second October 28, 1981 NCP minute which stated that Knight had been at the meeting and made the commitment. IV R. 124, 184-185; Government Exhibit 1. This second minute was taken to the United Southwest National Bank to assist in obtaining a loan for NCP. V R. 204.

During the questioning on March 8 before the grand jury, Larranaga requested an opportunity to have counsel present. Mr. Lutz, the United States Attorney, told Larranaga that questioning would stop after he identified certain records. Defendant's Exhibit D, at 29. Shortly thereafter Larranaga testified that he had presented all of NCP's minutes to the grand jury. IV R. 128, 189; Defendant's Exhibit D, at 38; Government Exhibit 4.

At trial, the Government contended that the minutes presented on March 8 were false and incomplete. The dispute concerned the apparent omission of facts concerning an October 28, 1981, NCP board meeting where David Knight made a commitment where David Knight made a commitment that Sangre would continue to occupy buildings NCP sought to acquire, according to minutes for that meeting furnished to United Southwest National Bank to get a loan for purchase of the buildings. See IV R. 118-120, 185; Order of District Court of January 4, 1984 at 3-4. David Knight's role in the affairs of NCP was also in dispute. The minutes brought by Larranaga indicated that Knight was present at only one NCP board meeting. V R. 230-31, 373; Defendant's Exhibit C-24 (Aug. 6, 1982). The testimony showed, however, that Knight was present at numerous such meetings. V R. 229, 267, 339, 343, 373.

Larranaga was indicted in two counts. The first count charged him with willfully and knowingly making a materially false statement and with submitting documents containing materially false declarations to the grand jury in violation of 18 U.S.C. § 1623. The second count charged him with obstruction of justice in violation of 18 U.S.C. § 1503 and 18 U.S.C. § 2. Larranaga was convicted on the first charge and acquitted on the second. I R. 265.

On appeal Larranaga contends: (1) the trial court erred in holding that materiality is a question of law, in instructing the jury that defendant's alleged misstatements were material to the grand jury's investigation, and in not submitting the question to the jury; (2) the evidence is not sufficient to support his conviction under § 1623; (3) the trial court unduly restricted the defendant's cross-examination of Ms. Garcia; (4) the court erred in denying admission of the grand jury transcript into evidence; (5) the court improperly denied defense counsel an opportunity to inspect the grand jury transcript on statements by Ernestine Encinias; and (6) the Government's closing argument was improper and prejudicial.

We find no reversible error.

II Materiality under § 1623: a question of law or fact

The defendant argues that because materiality is an essential element of an offense under § 1623, it must be decided by the trier of fact. We have recently said, however, that materiality in prejury cases under § 1623 is a question for the court to decide. See United States v. Girdner, 773 F.2d 257, 259 (10th Cir. 1985). Despite our contrary holdings under the false statement statute, 18 U.S.C. § 1001, we feel that the issue in prejury cases as to whether the defendant knowingly made a false material statement before the grand jury, see § 1623(a), involving the question whether it had a tendency to influence, mislead or hamper the grand jury in a matter which it had the authority to investigate, is logically one for the court as a matter of law. See United States v. Koonce, 485 F.2d 374, 380 (8th Cir. 1973); see also United States v. Girdner, 773 F.2d at 259. This question is proper for the court to determine.

We remain convinced that the materiality issue in prejury cases under § 1623 is properly for the court. See Sinclair v. United States, 279 U.S. 263, 298-99, 49 S.Ct. 268, 273-74, 73 L.Ed. 692 (1929). There was no infringement of the right to trial by jury by the trial court's handling of the issue of materiality.

III Sufficiency of the evidence

Defense counsel next contends that the evidence is insufficient to support the conviction. We will address separately the two theories advanced by the Government. The first theory is that the defendant produced incomplete, false and altered minutes for the grand jury on March 8. The second is that Larranaga falsely testified that the minutes produced for the grand jury were all the minutes of the Board of Directors or any subcommittees of the Board of NCP. Both theories were alleged in the indictment and submitted to the jury. V R. 444-46, 448. We conclude that the Government offered sufficient evidence on the first theory and thus uphold the conviction against this challenge, although we feel the proof on the second theory was defective.

A [18] Theory 1: the submission of false documents

Under the first theory, the Government must establish beyond a reasonable doubt that the defendant knowingly submitted false minutes to the grand jury. 18 U.S.C. § 1623(a) (1982). As we have held, the materiality of the false statements was an issue for the court to decide and we explain below that the proof was sufficient on that question. We now consider whether there was sufficient evidence, direct or circumstantial, together with the reasonable inferences that could be drawn, from which the jury could have found the defendant guilty beyond a reasonable doubt of knowingly submitting false declarations in the minutes. See, e.g., United States v. Yates, 470 F.2d 968, 970 (10th Cir. 1972).

1. Falsity and mens rea

The Government says that the minutes submitted to the grand jury were false in that they misrepresented the extent of Knight's participation in NCP's board meetings. Stanley-Smith and Garcia testified that Knight was usually in attendance, although the minutes indicate that Knight was present at only one meeting. II R. 230-31, 373. The defendant argues that the minutes were literally correct because NCP had no obligation to identify anyone as present other than the directors. We disagree.

If we assume that NCP was not obligated to identify visitors at its meetings, nonetheless the minutes purport to identify every person in attendance. See, e.g., Government's Exhibit 1 ("others present"), 3 (headnote lists three persons in attendance, one of whom was not a director); Defendant's Exhibit C-9 ("present"), C-19 ("those present"). The implication, of course, is that anyone not identified in these minutes was absent. Knight, however, attended many of these meetings although he was not listed in the minutes. The minutes for October 28, 1981, and April 23, 1982, are particularly misleading. The minutes for October 28 states that Garcia was the only non-board member to attend this meeting. Government Exhibit 2. There is no mention of David Knight. In fact, however, Knight was present at the meeting and gave a verbal commitment that Sangre would continue to lease certain buildings from NCP. IV R. 120, V R. 204-05, 279, 299, 372-73; Government Exhibit 1; Defendant's Exhibit C-1. The minute for April 23 also fails to mention Knight's presence at the meeting. In addition, it states that "an anonymous source will arrange a loan with Western Bank for $25,000 for [NCP]." V R. 236, 346, 382; Government Exhibit 3; Defendant's Exhibit C-15. Ms. Encinias testified, however, that "at the meeting it was disclosed that Mr. Knight was, in fact, making the $25,000 loan." V R. 347. Of course, if this testimony was true, the source of the loan was not "anonymous." Encinias' testimony thus provided the jury with sufficient evidence to conclude that the April 23 minutes were false.

The evidence is also sufficient to support a finding that the defendant knew the minutes were false. The trier of fact may infer this element of knowledge from the surrounding circumstances. See, e.g., United States v. Peters, 625 F.2d 366, 369 (10th Cir. 1980). We think the Government's evidence supported such an inference here. The Government pointed to the minutes of October 28, 1981, and April 23, 1982. If Larranaga had read the rough notes given to Garcia, he would have known that they did not accurately disclose Knight's participation at those meetings. The crucial question in the case, then, is whether Larranaga knew what the notes said.

The evidence supports an affirmative answer. First, after Larranaga received the first subpoena, he and his associates met with Knight on three occasions to prepare the documents requested by the grand jury. V R. 225-26, 228-29, 367. Several of the board members brought rough notes to the sessions. V R. 226-27.

Second, Garcia testified that Knight was omitted from all the minutes in part because he would say "I'm not here" at the meetings. V R. 279-80. The implication, of course, is that Larranaga, like the other NCP directors, knew that Knight was omitted from the notes.

Finally, the evidence indicates that defendant Larranaga knew that Knight had made the $25,000 loan. Ms. Encinias testified that the lender's identity was announced during the meeting. V R. 347. In addition, each other person attending the April 23 meeting, except the defendant, testified that they knew on that date that Knight was the person making the loan. V R. 236, 346, 381.

We hold that there was sufficient evidence for the jury to conclude that Larranaga knowingly submitted false minutes to the grand jury on March 8. Thus, we will not disturb the jury's findings with respect to falsity or mens rea.

2. Materiality

Defense counsel also argues that the Government must prove materiality beyond a reasonable doubt, which is a jury question. Defendant-Appellant's Reply Brief at 3. We have rejected the argument that the question was one for the jury. We further conclude that the Government did establish materiality sufficiently for the trial court to conclude that the misstatements of Larranaga were material to the grand jury's investigation, as the jury was instructed. Since materiality is a question of law, as we hold, there was no burden to prove that element beyond a reasonable doubt. See, e.g., United States v. Armilio, 705 F.2d 939, 941 n. 5 (8th Cir.), cert. denied, 464 U.S. 891, 104 S.Ct. 235, 78 L.Ed.2d 227 (1983).

The foreperson of the grand jury testified that it was investigating a possible misuse of federal funds by Sangre. In the course of its investigation, the grand jury became increasingly interested in the relationship between NCP, Sangre, and David Knight, and the jurors suspected Knight was an important influence in the decision-making processes of NCP. IV R. 115-118. The investigation of these relationships was clearly within the grand jury's powers. Moreover, the misrepresentation of Knight's participation in the meetings was capable of influencing this investigation. See United States v. Girdner, 773 F.2d 257, 259-60 (10th Cir. 1985). Thus, we think the Government presented sufficient evidence to support the trial court's conclusion of materiality on the first theory of a criminal violation — the submission of false minutes to the grand jury on March 8 — and the court's instruction to that effect. V R. 448.

B. Theory 2: false testimony before the grand jury

The Governments second theory is that Larranaga gave false testimony when he said that he had presented all of NCP's minutes. The dialogue was as follows:

Q. Then next we subpoenaed the minutes of the Board of directors' meeting. We have marked as Exhibit 15. Are these all of the minutes of the Board of Directors' meeting or any other subcommittees of that board?

A. Yes, sir.

IV R. 110-11, 139, 140, 189; V R. 445; Government Exhibit 4. The Government argued that his testimony was false for two reasons. First, it said that when Larranaga initially appeared before the grand jury, he presented only the minute for October 28 that Garcia had typed although a second minute relating the occurrences at the same meeting was then in NCP's files. V R. 342. The Government also argued that the rough notes on napkins and legal pads were "minutes," and that Larranaga's response implied that such papers had all been given to the grand jury.

We do not think the Government's argument is tenable in light of the construction of § 1621 in Bronston v. United States, 409 U.S. 352, 93 S.Ct. 595, 34 L.Ed.2d 568 (1973) (perjury conviction may not rest on answer which is literally true but not responsive to question and arguably misleading by negative implication). There the court rejected the Government's argument that the perjury statute be construed broadly. It reversed a conviction in somewhat similar circumstances, being unconvinced that "Congress intended to extend the coverage of § 1621 to answers unresponsive on their face but untrue only by `negative implication' . . . Precise questioning is imperative as a predicate for the offense of perjury." Id. at 361-62, 93 S.Ct. at 601-02.

Here the questioner could have precisely asked Larranaga if there were any related rough notes, memoranda or the like dealing with the meetings covered by the minutes. He could also have inquired whether there were any other minutes detailing the events of the same meetings in question. Leaving the matter as it was permitted the answer to be ambiguous in the context of these facts, and untrue by its "negative implication." We must agree that the theory that perjury was committed by Larranaga's one answer is untenable under the perjury statute as construed in Bronston. See also United States v. Cowley, 720 F.2d 1037, 1042-43 (9th Cir. 1983).

C. The sufficiency of one theory to support the conviction

The jury here returned a general verdict of guilty on the perjury charge. Thus its decision to convict might arguably have rested on the Government's second theory, on which we hold the evidence was fatally defective. We therefore feel we should consider whether the latter possibility requires a reversal of the conviction.

The Supreme Court has not definitively answered this question. It has held that reversal is required "in cases where the verdict is supportable on one ground, but not on another, and it is impossible to tell which ground the jury selected." Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1073, 1 L.Ed.2d 1356 (1957), overruled on other grounds, Burks v. United States, 437 U.S. 1, 17-18, 98 S.Ct. 2141, 2150-51, 57 L.Ed.2d 1 (1978); see also Cramer v. United States, 325 U.S. 1, 36 n. 45, 65 S.Ct. 918, 935 n. 45, 89 L.Ed. 1441 (1945) (reversal proper "[s]ince it is not possible to identify the grounds on which Cramer was convicted").

In some instances the courts of appeals have refused to speculate on the basis of the conviction. See United States v. Sales, 725 F.2d 458, 459 (8th Cir. 1984) (quoting Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1073, 1 L.Ed.2d 1356 (1957)); United States v. Carman, 577 F.2d 556, 566 (9th Cir. 1978). However, in other instances convictions have been upheld where the reviewing court could determine that there was sufficient evidence to sustain the conviction on one theory; there was a caveat where an overwhelming amount of evidence relevant to only the unproved theory may have prejudiced the defendant. See United States v. Papadakis, 510 F.2d 287, 297 (2d Cir.), cert. denied, 421 U.S. 950, 95 S.Ct. 1682, 44 L.Ed.2d 104 (1975); United States v. Tanner, 471 F.2d 128, 140 (7th Cir.) (upholding conspiracy conviction "so long as one of the objects of the conspiracy is unchallenged"), cert. denied, 409 U.S. 949, 93 S.Ct. 269, 34 L.Ed.2d 220 (1972).

We have reversed convictions in such instances. See United States v. Radetsky, 535 F.2d 556, 573 (10th Cir. 1976) (overturning convictions for making false statements when an immaterial alleged misstatement was submitted to jury and could have been basis of general verdict), cert. denied, 429 U.S. 820, 97 S.Ct. 68, 50 L.Ed.2d 81 (1976); see also United States v. Dota, 482 F.2d 1005, 1006 (10th Cir.) (stating that if evidence is insufficient regarding any of defendant's alleged misstatements, "a reversal is necessary under the general verdict"), cert. denied, 414 U.S. 1071, 94 S.Ct. 583, 38 L.Ed.2d 477 (1973).

However, we conclude that where we can confidently determine that the jury relied on the theory validly supported by the evidence, even though some lesser consideration may also have been given to the theory not sufficiently proven to support a conviction alone, then the judgment need not be disturbed. See United States v. Irwin, 654 F.2d 671, 685 (10th Cir. 1981), cert. denied, 455 U.S. 1016, 102 S.Ct. 1709, 72 L.Ed.2d 133 (1982). Here we have no difficulty in concluding that the jury must have relied primarily on the first theory. The Government placed its major emphasis on the omission of Knight's name in NCP's minutes. The evidence sometimes overlapped, but the greater weight of the Government's evidence was relevant to the omission of Knight's involvement in NCP's affairs. In addition, the Government in its closing argument pressed the Knight omission from the minutes as its major argument.

In these circumstances we hold that the conviction need not be set aside because of the defect in the proof on the theory that the defendant gave false testimony before the grand jury. Hence the conviction should not be reversed for insufficiency of the evidence.

IV The cross-examination of Garcia

The defendant next argues that the trial court unduly restricted his cross-examination of Garcia. Specifically he contends that the trial court erred in denying his offer of Garcia's immunity agreement into evidence and in preventing inquiry into her refusal to testify before the grand jury. We reject both contentions.

A. Garcia's Immunity Agreement

The trial court's exclusion of the immunity agreement is erroneous only if it infringed on the defendant's Sixth Amendment right of confrontation or constituted an abuse of discretion. See United States v. Wood, 695 F.2d 459, 464 (10th Cir. 1982); United States v. Alderete, 614 F.2d 726, 728 (10th Cir. 1980). We hold that exclusion of the agreement did not constitute error in either respect.

In doing so, we recognize the important interest that an accused has in effective cross-examination. See Douglas v. Alabama, 380 U.S. 415, 418, 85 S.Ct. 1074, 1076, 13 L.Ed.2d 934 (1965); Pointer v. Texas, 380 U.S. 400, 403, 85 S.Ct. 1065, 1067-68, 13 L.Ed.2d 923 (1965). The right of confrontation, however, is not without limits. Here the question is "whether the jury had sufficient information to make a discriminating appraisal of the witness' motives and bias." United States v. Swingler, 758 F.2d 477, 498 (10th Cir. 1985) (quoting United States v. De Gudino, 722 F.2d 1351, 1354 (7th Cir. 1983)); United States v. Nunez, 668 F.2d 1116, 1122 (10th Cir. 1981). The trial court concluded that the jury had sufficient information to make a discriminating appraisal of Garcia's credibility. We agree.

On direct examination, Garcia admitted that she had entered into an immunity agreement with the Government. V R. 284. She testified that the agreement obligated her to testify truthfully in return for the Government's dismissal of charges of aiding and abetting an obstruction of justice. V R. 285. The defense counsel then extensively cross-examined Garcia about the agreement. Garcia said that the Government had charged her with falsifying documents along with Larranaga. Garcia also testified that the agreement required her to cooperate fully with the Government and volunteer anything that might assist in its prosecution against Larranaga. V R. 288-89. Her testimony stated clearly her reason for entering the agreement:

Q. Now, you entered into this agreement in order to have the charge that you were going to trial on dismissed, is that right?

A. That's correct.

V R. 289.

We cannot see what the immunity letter could have added to this cross-examination. The agreement was relevant only insofar as it shed light on the witness' possible bias. The provisions themselves, however, were of little intrinsic value; the inference of bias arises from how the witness perceives he will benefit from the agreement. The trial judge did not restrict the inquiry as to Garcia's understanding of the agreement, but merely prevented defense counsel from introducing the provisions themselves. In some instances this could be prejudicial, but we see no impairment of the defendant's case here.

We conclude that the trial court's ruling did not violate that defendant's constitutional right of confrontation or amount to an abuse of discretion. See United States v. Wood, 695 F.2d at 464-65.

B. Garcia's prior assertion of her privilege against self-incrimination

The defendant also claims that the trial court erred in preventing cross-examination into Garcia's prior assertion of her privilege against self-incrimination. Larranaga argues that this restriction violated his Sixth Amendment rights of confrontation and effective assistance of counsel. We disagree.

The threshold requirement for the admission of evidence is that it have some probative value. Fed.R.Evid. 401 402. We have long held, however, that the jury cannot draw inferences from a prosecution witness' decision to invoke his Fifth Amendment privilege. See, e.g., United States v. McClure, 734 F.2d 484, 491 (10th Cir. 1984); United States v. Hart, 729 F.2d 662, 670 (10th Cir. 1984), cert. denied, ___ U.S. ___, 105 S.Ct. 914, 83 L.Ed.2d 927 (1985). Thus, Garcia's prior refusal to testify was inadmissible because it lacked legitimate probative value.

The Sixth Amendment rights to confrontation and effective assistance of counsel do not dictate otherwise. The amendment does not require the trial court to admit evidence that the jury could not otherwise consider. See United States v. Nunez, 668 F.2d 1116, 1122 (10th Cir. 1981) (not every invocation of privilege against self-incrimination by a witness results in denial of defendant's Sixth Amendment rights). In other contexts we have held that one's earlier invocation of his constitutional privilege cannot be used at trial. See United States v. De La Luz Gallegos, 738 F.2d 378, 382 (10th Cir.), cert. denied, ___ U.S. ___, 105 S.Ct. 574, 83 L.Ed.2d 514 (1984); United States v. Bridwell, 583 F.2d 1135, 1138 (10th Cir. 1978); see also United States v. Natale, 526 F.2d 1160, 1171 (2d Cir. 1975), cert. denied, 425 U.S. 950, 96 S.Ct. 1724, 48 L.Ed.2d 193 (1976). We see no reason to hold otherwise here.

V. Exclusion of Larranaga's grand jury transcript

The defendant next argues that the trial court erred in excluding his grand jury transcript of March 8. He bases this challenge on Federal Rule of Evidence 106, which codifies the common-law doctrine of "completeness." We think the trial court acted within its discretion in excluding the evidence.

Early in the trial the Government introduced Larranaga's March 8 statement that he had presented all of NCP's minutes to the grand jury. IV R. 110-11; Government Exhibit 4. The defendant did not object. IV R. 111. Later, in its cross-examination of Larranaga, the Government referred to another passage in the March 8 transcript. This passage contained Larranaga's denial before the grand jury that Sangre had agreed to lease certain properties before they were purchased by NCP. V R. 375-76. Again, the defendant failed to object. V R. 376-81. During re-direct examination, however, defense counsel offered the entirety of Larranaga's March 8 testimony, asserting Federal Rule of Evidence 612 as a ground for admission. V R. 391-93. The offer was rejected.

On appeal, the defendant argues that the transcript was admissible under Federal Rule of Evidence 106. This rule provides: "When a writing or recorded statement or part thereof is introduced by a party, an adverse party may require him at that time to introduce any other part or any other writing or recorded statement which ought in fairness to be considered contemporaneously with it." Fed.R.Evid. 106. Defendant did not follow the procedure outlined in rule 106 "at that time" when the question and answers were introduced. Thus defendant's reliance on Rule 106 is misplaced.

Moreover, even if Rule 106 had been properly invoked and followed at trial, there was no error in the refusal to admit the entire transcript when defense counsel offered it during her redirect examination of defendants. There are no portions which should have been admitted "in fairness" to the defendant under the completeness doctrine of Rule 106, and the ruling was not an abuse of discretion. See United States v. Mulligan, 573 F.2d 775, 778 (2d Cir.), cert. denied, 439 U.S. 827, 99 S.Ct. 99, 58 L.Ed.2d 120 (1978).

VI. Disclosure of Encinias' grand jury transcript

Defense counsel next contends that the trial court committed reversible error in denying her request to inspect Encinias grand jury transcript. We disagree.

Encinias' testimony on direct examination was brief. V R. 325-35. She focused on the gathering of NCP's records for presentation to the grand jury, V R. 326-31, 332-34, and Knight's $25,000 loan to NCP, V R. 331-32. The most damaging portion of her testimony came on cross-examination. There she testified that she had found an additional set of minutes between Larranaga's first and second appearances before the grand jury. V R. 342. On the basis of this testimony, the defense suggested that Encinias had found the missing minute for October 28. As a result, the defense said that Larranaga could not have known the second minute existed when he first testified before the grand jury. V R. 433-34 (Defendant's closing argument).

The Government, however, also attempted to impeach Encinias with her earlier grand jury testimony. First, the Government referred to Encinias' previous denial that Knight was present when the NCP board decided to have the minutes typed. IV R. 337-38 see II R. 339-40 (Encinias' grand jury transcript). She admitted that this testimony was false. V R. 338-39.

Second, the Government quizzed Encinias about the number of NCP meetings that Knight had attended. She told the grand jury that Knight had attended less than one-third of the meetings. V R. 344. On cross-examination, however, she again admitted that this testimony was false. V R. 345.

During the Government's second use of the transcript, the defense requested an opportunity to inspect the entire document pursuant to Rules 612 and 613 of the Federal Rules of Evidence. V R. 343-44, 348. The trial court denied this request, confining disclosure to the pages actually used by the Government during cross-examination. V R. 337, 344, 348.

We will address the evidentiary issues separately.

A. Rule 612

We do not believe that Rule 612 required disclosure of the entire transcript. This rule provides in part:

[I]f a witness uses a writing to refresh his memory for the purpose of testifying, either —

(1) while testifying, . . .

an adverse party is entitled to have the writing produced at the hearing, to inspect it, to cross-examine the witness thereon, and to introduce in evidence those portions which relate to the testimony of the witness.

Fed.R.Evid. 612.

The rule is limited. It only requires disclosure of the passage actually used by the witness, and other portions relating to the same subject matter. See Fed.R.Evid. 612 advisory committee note; United States v. Costner, 684 F.2d 370, 373 (6th Cir. 1982); United States v. Wright, 489 F.2d 1181, 1188-89 (D.C. Cir. 1973); National Dairy Products Corp. v. United States, 384 F.2d 457, 460 (8th Cir. 1967), cert. denied, 390 U.S. 957, 88 S.Ct. 1032, 19 L.Ed.2d 1151 (1968). In requesting the trial court to order disclosure, defense counsel overstated the requirements contained in Rule 612. She asserted a right to inspect the entire transcript, rather than just the relevant portions. V R. 343, 348. The trial court properly denied this request, confining disclosure to those pages actually used by the Government. V R. 344, 348.

We find no reversible error in this ruling.

B. Rule 613

The defendant also relied on Federal Rule of Evidence 613(a) in making the request for the entire transcript of Encinias' testimony. This rule provides: "In examining a witness concerning a prior statement made by him, whether written or not, the statement need not be shown nor its contents disclosed to him at that time, but on request the same shall be shown or disclosed to opposing counsel." Fed.R. Evid 613(a). Assuming, arguendo, that the ruling violated Rule 613(a), we do not believe the error requires reversal. The record discloses no material that defense counsel could have used effectively to clarify the inconsistencies in Encinias' testimony. The Government first referred to the witness' prior testimony that Knight had attended less than one-third of NCP's meetings. II R. 345-46 (grand jury transcript); see V R. 344 (trial transcript). The grand jury transcript contains only two other references to Knight's presence at the meetings. Both of these meetings involved NCP's decision to lease certain telephone systems to Sangre. Encinias said that Knight was present at one meeting, II R. 395, and absent from the other, II R. 405. The passages bear only a remote relation to the portion used by the Government. It seems difficult to imagine how the two other passages could have shed light on the Government's reference to the transcript.

The Government also used Encinias' prior testimony that Knight was present when the NCP board decided to have Garcia type the minutes. II R. 339-40 (grand jury transcript); see V R. 337-38 (trial transcript). The grand jury transcript contains no other references to this subject.

Thus, disclosure of the document would not have helped defense counsel in rehabilitating the witness. Even if the trial court erred, we think it inconceivable that a different ruling would have affected the outcome. Under such circumstances, we hold that any possible error was harmless. See Rule 52(a), Fed.R.Cr.P.; Rosenberg v. United States, 360 U.S. 367, 371, 79 S.Ct. 1231, 1234, 3 L.Ed.2d 1304 (1959); see also Marcus v. United States, 422 F.2d 752, 754 (5th Cir. 1970) (conviction not reversible if denial of right to inspect memoranda used by witness does not affect defendant's substantial rights).

VII The claim of prosecutorial misconduct

Finally, the defendant contends that the Government's closing argument was improper at several points. Defense counsel argues that the prosecutor prejudicially stated his opinion on the guilt of the defendant and improperly argued about the importance of the grand jury system, among other things, encouraging the jury to return a conviction by impermissible arguments The trial judge rejected the objection made to the comments and denied a motion for a mistrial.

We hold that the closing remarks did not constitute such an infringement of the defendant's rights as to call for a reversal. The prosecuting attorney did at one point express a personal opinion that perjury was committed, which regrettably violated the rule against his expression of an opinion on the defendant's guilt. However, the objectionable comment was brief and no objection was made then. The only objection to the argument was made two pages later in the transcript following a portion of the argument stressing the importance of the case to the administration of justice in the district and the functioning of the grand jury process. Considering the objectionable comment about the commission of perjury and the argument of the prosecuting attorney as a whole, we cannot agree that there was prejudice created which calls for a reversal.

In sum, we conclude that no reversible error was demonstrated.

AFFIRMED.